Interest Rate Calculator — Find Annual Rate from Principal & Final Amount
Enter the starting amount, the final amount and the investment period and this calculator works backwards to find the annual interest rate — telling you the rate that would grow the principal to the final value in the given time, using either simple or compound interest.
years
Interest type
Rate that grows the principal to the final amount in the given period
- 1
Growth ratio
1,500 ÷ 1,000 = 1.5 - 2
ᵗ√ root (CAGR factor)
1.5^(1 ÷ 5) = 1.0845Taking the t-th root normalises total growth to a single-year rate. - 3
Annual interest rate (CAGR)
1.0845 − 1 = 8.4472 %
How does this calculator work?
To find the annual rate: Simple interest → r = (A/P − 1) / t. Compound (CAGR) → r = (A/P)^(1/t) − 1. Enter starting amount, final amount and years, pick interest type. The result is the implied annual rate that achieves that growth — identical to CAGR for compound mode.
Formula
How this is calculated
Most interest calculators go forward: give them a rate and they show you the final amount. This calculator does the inverse — it takes the start and end amounts and the period and solves for the implied annual rate. Under simple interest the relationship is A = P(1 + r·t), which rearranges to r = (A/P − 1)/t. Under annual compound interest it is A = P(1 + r)^t, giving r = (A/P)^(1/t) − 1.
For compound interest, this implied rate is also called the Compound Annual Growth Rate (CAGR) and is widely used to compare investment performance across different time horizons. For example, if a fund grew from 10,000 to 18,000 over 7 years, the CAGR is (18000/10000)^(1/7) − 1 ≈ 8.77 %, regardless of how bumpy the returns were in individual years.
Note that this calculator assumes a single lump sum at the start with no intermediate deposits or withdrawals. If cash flows occur throughout the period (such as with a savings plan or dividend reinvestment), the implied rate would instead be an internal rate of return (IRR), which requires numerical solving not covered here. The result shown here is also a nominal annual rate — taxes, fees and inflation are not deducted.
Frequently asked questions
For the same start/end amounts and time period, the simple interest rate will always be higher than the compound rate. That is because with compound interest, interest itself earns interest over time, so a lower rate achieves the same total growth. If the investment actually compounds, use the compound option for an accurate rate.
Yes — in compound mode this calculator computes the CAGR (Compound Annual Growth Rate): the single constant annual rate that would produce the same overall growth as the observed start-to-finish change. CAGR smooths out volatility and is the standard for comparing funds or assets over different periods.
Monthly compounding uses A = P(1 + r/12)^(12t). Solving for r gives r = 12 × ((A/P)^(1/(12t)) − 1). The resulting monthly nominal rate, annualised, will be slightly lower than the annual compound rate for the same growth. This calculator uses annual compounding as the standard — for monthly compounding, use a compound interest calculator with the rate you find here and verify the final amount.
Also known as
TG we-Calculate Editorial Team. (2026). Interest Rate Calculator — Find Annual Rate from Principal & Final Amount [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/interest-rate-calculator
TG we-Calculate Editorial Team. "Interest Rate Calculator — Find Annual Rate from Principal & Final Amount." TG we-Calculate. 2026. https://we-calculate.com/calculator/interest-rate-calculator.
TG we-Calculate Editorial Team, "Interest Rate Calculator — Find Annual Rate from Principal & Final Amount," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/interest-rate-calculator
@misc{wecalculate_interest_rate_calculator, title = {Interest Rate Calculator — Find Annual Rate from Principal & Final Amount}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/interest-rate-calculator}}, year = {2026}, note = {TG we-Calculate} }
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